Power Sum

Probability Level 5

Find {a1,,ak}{1,2,3,4,5}1a1ak\displaystyle \sum_{\{a_{1}, \ldots, a_{k}\} \subseteq \{1, 2, 3, 4, 5\}} \frac{1}{a_{1} \cdots a_{k}}, where the sum is over all nonempty subsets of of the set {1,2,3,4,5}\{1, 2, 3, 4, 5\}.

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